Simplified lattice model for polypeptide fibrillar transitions

Polypeptide fibrillar transitions are studied using a simplified lattice model, modified from the three-state Potts model, where uniform residues as spins, placed on a cubic lattice, can interact with neighbors to form coil, helical, sheet, or fibrillar structure. Using the transfer matrix method and numerical calculations, we analyzed the partition function and construct phase diagrams. The model manifests phase transitions among coil, helix, sheet, and fibril through parameterizing bond coupling energy epsilon(h), epsilon(s), epsilon(f), structural entropies s(h), s(s), s(f) of helical, sheet, and fibrillar states, and number density rho. The phase diagrams show the transition sequence is basically governed by epsilon(h), epsilon(s), and epsilon(f), while the transition temperature is determined by the competition among epsilon(h), epsilon(s), and epsilon(f), as well as s(h), s(s), s(f), and rho. Furthermore, the fibrillation is accompanied with an abrupt phase transition from coil, helix, or sheet to fibril even for short polypeptide length, resembling the feature of nucleation-growth process. The finite-size effect in specific heat at transitions for the nonfibrillation case can be described by the scaling form of lattice model. With rich phase-transition properties, our model provides a useful reference for protein aggregation experiments and modeling.